6.X1

Some experts believe that at least 1 in 3 tractor-trailer units has a hazardous mechanical condition related to the braking system. A survey of 50 tractor-trailer units passing through a weighing station confirmed that 19 had a potentially serious braking system problem.

a) Are the assumptions for a valid CI met for these data?

b) Compute a 95% CI for the true proportion of tractor-trailer units with a serious braking issue and state an interpretation. Why might a researcher think that this interval was not very informative? 

Suppose you are testing Ho: p=1/3 vs. Ha: p>1/3 at the alpha=.05 level of significance.
c) Write the rule for rejecting Ho in terms of z-scores. 
d) Write the rule for rejecting Ho in terms of p_hat. 
e) Find the probability of a Type II error if the true population proportion of units with a breaking problem is p=.46 [i.e., find Beta(.46)].